Find the percentage change of copper wire if its length is increased by 0.1%
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The resistance will be increased by 0.2%. Explanation is given below:
Equation of the resistance is:
R = ρ*L/A (ρ is resistivity, L is length and A is area of the conductor)
Let initial area be A1, length be L1 and Resistance be R1.
Therefore equation of initial resistance R1 is:
R1 = ρ*L1/A1
After stretching, the length increases by 0.1% ie. 1.001 times. As volume is same, area is expected to be reduced by inverse of this i.e. 1/1.001 times. Therefore R2 (new value of resistance) will be:
R2 = ρ*(1.01L1)/(A1/1.001) = ρ*(1.001*1.001)*L1)/(A1) = ρ*1.002*L1/A1
Ratio of new resistance to original resistance is:
R2/R1 =(ρ*1.002*L1/A1)/(ρ*L1/A1)
= 1.002
= 100.2%. Hence percentage change is 0.2% increase.
Equation of the resistance is:
R = ρ*L/A (ρ is resistivity, L is length and A is area of the conductor)
Let initial area be A1, length be L1 and Resistance be R1.
Therefore equation of initial resistance R1 is:
R1 = ρ*L1/A1
After stretching, the length increases by 0.1% ie. 1.001 times. As volume is same, area is expected to be reduced by inverse of this i.e. 1/1.001 times. Therefore R2 (new value of resistance) will be:
R2 = ρ*(1.01L1)/(A1/1.001) = ρ*(1.001*1.001)*L1)/(A1) = ρ*1.002*L1/A1
Ratio of new resistance to original resistance is:
R2/R1 =(ρ*1.002*L1/A1)/(ρ*L1/A1)
= 1.002
= 100.2%. Hence percentage change is 0.2% increase.
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WHEN LENGTH IS INCREASED BY 0.1%, THEN AREA OF CROSS SECTION ALSO CHANGES.
JUST EXPRESS AREA IN TERMS OF MASS AND DENSITY OF COPPER BY USING THE FORMULA DENSITY=MASS/VOLUME
AND U WILL GET YOUR ANSWER
JUST EXPRESS AREA IN TERMS OF MASS AND DENSITY OF COPPER BY USING THE FORMULA DENSITY=MASS/VOLUME
AND U WILL GET YOUR ANSWER
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